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Volume

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Prisms

b is for bredth, or width of the cuboid. l is for length, and h is for height

You already know that the volume of a cuboid is length by its width by its height (l × w × h).

The area of the shaded end of the cuboid (the cross section) is w × h, so you can also say that the volume of a cuboid is:

area of cross section × length

Different types of prism

This formula works for all prisms:

3 prisms. 1 is a cylinder, 2 is a triangle based prism and 3 is an L shape prism
  1. volume of a cylinder = area of circle × length
  2. volume of triangular prism = area of triangle × length
  3. volume of 'L'-shaped prism = area of 'L'-shape × length
Question

Q1. What is the volume of this triangular prism?

2cm (h) x 5cm (b) x 4cm (l)

Q2. What is the volume of this prism?

L shape
Answer

A1. volume = area of triangle × length
= 1/2× 2 × 5 × 4
= 20cm3

A2. The area of the cross section is 5cm2 and the length is 8cm, so the volume is 5 × 8 = 40 cm3

Remember that the volume is the area of the cross section × the length.

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Activity

Volume activity

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